You can get some sinew from moose and bear, or a little plant fiber from dogbane and cattail. This is slow, so not practical.
The peasant is yanked from his idyllic village to the realm of Eastern Cannibal Pagan Empire. He is not going to build a cottage and raise hog, at least not now. Survival comes first, then style and conduct. I'd say one just does what an ordinary survivor does. Skirmishing zombies around the town, getting clothing, a lighter, and a makeshift crowbar.
Wool cloak already covers the torso well. What one wants are pants, boots, and some curtain sheets for gloves, hat, and scarf.
Mi-go bites hard but runs fast but it's actually slower than you. Alternating between running and walking, you can escape mi-go.